It is by now a standard fact that every 4d \({\cal N}=1\)  theory with a continuous \(R\) -symmetry can be studied on the spatial manifold \(S^3\)  while preserving four (time-independent) supercharges [1]}, [2]}, [3]}, [4]}, see also the reviews [5]}, [6]}. The virtue of having the theory in compact space is that the spectrum is discrete and the states are easier to count. One can define the Hamiltonian by picking a supercharge \(\mathcal {Q}\)  and declaring the Hamiltonian to be proportional to \(\lbrace  \mathcal {Q},{\mathcal {Q}}^\dagger \rbrace  \) . It is particularly interesting to consider the states which have zero energy. Those, as usual, need to be annihilated by \( \mathcal {Q}\) , \(\mathcal {Q}^\dagger \) .
